Why there is no End to Music

in math •  8 years ago 

Have you ever wondered how there can be over 35 million different and DISTINCT songs on iTunes ?
click to see article about how many songs iTunes has

Well, its even crazier when you search in google for : "How many songs are there in the world"
Spoiler alert:
97 million is the answer you get See here

In a matter of fact, mathematically speaking 97 millions songs is literally nothing compared to how many different songs can exist.

Lets start our Maths by looking at a pretty standard Audio CD which holds 700 MB or round about 80 minutes of Audio.

Also, lets consider you have to change 1 bit to create a new song.

Before we look how many ways there are to rearrange 700 MB. lets look at 8 bits ( or a Byte)

00000000 in binary is obviously 0
00000001 is 1
00000010 is 2 in decimal system

so counting all the way up to
11111111 equals 255

Meaning that there are 256 possible values (because 0 is also a value)

An easier attempt to calculate the possible values would have been to have 2 to the power of 8.

Why?? you might ask.

With a single bit, you can display 2 different values (1 and 0)
with a second one you can display twice as much.
with a third one you have twice as much again.
and because you have 8 bits you can calculate 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 or 2 to the power of 8
or

                8
         2

Now if we want to know how many different song files there can be on a 700 MB disk we need to know that you need 1024 Bytes to get 1 Kilobyte and again 1024 Kilobytes to get 1 Megabyte

also 8 Bits is equal to 1 Byte
so we have

                       700
               1024
         1024
      8                                                             
  2             

or

            (8*1024*1024*700)                                                 
     2                                                 

different ways

according to http://mrob.com/pub/comp/hypercalc/hypercalc-javascript.html the result is

                             1767655840
        8.0684 * 10

which is a number with 1767655840 digits
80
in comparison: the number of atoms in the visible universe is guessed to be 10 ^ which has 80 digits.

and 92 Million is just 8 digits long.

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